The Distribution of Spacings Between the Fractional Parts of ndα

Martino Fassina; Sun Kim; Alexandru Zaharescu

doi:10.1093/imrn/rnab022

The Distribution of Spacings Between the Fractional Parts of n^dα

Martino Fassina^*
, Sun Kim
, Alexandru Zaharescu

^*Corresponding author for this work

Department of Mathematics

University of Vienna
University of Illinois at Urbana-Champaign
Romanian Academy

Research output: Contribution to journal › Journal article › peer-review

2 Scopus citations

Abstract

We study the distribution of spacings between the fractional parts of n dα . For α of high enough Diophantine type we prove a necessary and sufficient condition for n dα \mod 1, 1≤ n≤ N, to be Poissonian as N\to ∞ along a suitable subsequence.

Original language	English
Pages (from-to)	10555-10585
Number of pages	31
Journal	International Mathematics Research Notices
Volume	2022
Issue number	14
DOIs	https://doi.org/10.1093/imrn/rnab022
State	Published - 2022.07.1

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1093/imrn/rnab022

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title = "The Distribution of Spacings Between the Fractional Parts of ndα",

abstract = "We study the distribution of spacings between the fractional parts of n dα . For α of high enough Diophantine type we prove a necessary and sufficient condition for n dα \textbackslash{}mod 1, 1≤ n≤ N, to be Poissonian as N\textbackslash{}to ∞ along a suitable subsequence.",

author = "Martino Fassina and Sun Kim and Alexandru Zaharescu",

year = "2022",

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doi = "10.1093/imrn/rnab022",

language = "English",

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T1 - The Distribution of Spacings Between the Fractional Parts of ndα

AU - Fassina, Martino

AU - Kim, Sun

AU - Zaharescu, Alexandru

PY - 2022/7/1

Y1 - 2022/7/1

N2 - We study the distribution of spacings between the fractional parts of n dα . For α of high enough Diophantine type we prove a necessary and sufficient condition for n dα \mod 1, 1≤ n≤ N, to be Poissonian as N\to ∞ along a suitable subsequence.

AB - We study the distribution of spacings between the fractional parts of n dα . For α of high enough Diophantine type we prove a necessary and sufficient condition for n dα \mod 1, 1≤ n≤ N, to be Poissonian as N\to ∞ along a suitable subsequence.

UR - https://www.scopus.com/pages/publications/85134626202

U2 - 10.1093/imrn/rnab022

DO - 10.1093/imrn/rnab022

M3 - Journal article

AN - SCOPUS:85134626202

SN - 1073-7928

VL - 2022

SP - 10555

EP - 10585

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 14

ER -

The Distribution of Spacings Between the Fractional Parts of n^dα

Abstract

Quacquarelli Symonds(QS) Subject Topics

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